Revisiting displacement functions in three-dimensional elasticity of inhomogeneous media

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:46

Article

Kashtalyan, M.¹  Rushchitsky, J. J.² 

[1] Univ Aberdeen, Sch Engn, Ctr Micro & Nanomech CEMINACS, Fraser Noble Bldg, Aberdeen AB24 3UE, Scotland

[2] Natl Acad Sci Ukraine, Timoshenko Inst Mech, UA-03680 Kiev, Ukraine

关键词: Elasticity;    Linear elasticity;    Three-dimensional elasticity solution;    Analytical solutions;    Functionally graded materials;    Transversely isotropic material;   

DOI  :  10.1016/j.ijsolstr.2009.06.001

来源: Elsevier

【 摘 要 】

The paper presents a three-dimensional solution to the equilibrium equations for linear elastic transversely isotropic inhomogeneous media. We assume that the material has constant Poisson's ratios, and its Young's and shear moduli have the same functional form of dependence on the co-ordinate normal to the plane of isotropy. We show, apparently for the first time, that stresses and displacements in such an inhomogeneous transversely isotropic elastic solid can be represented in terms of two displacement functions which satisfy the second- and fourth-order partial differential equations. We examine and discuss key aspects of the new representation; they include the relationship between the new displacement functions and Plevako's solution for isotropic inhomogeneous material with constant Poisson's ratio as well as the application of the new representation to some important classes of three-dimensional elasticity problems. As an example, the displacement function is derived that can be used to determine stresses and displacements in an inhomogeneous transversely isotropic half-space which is subjected to a concentrated force normal to a free surface and applied at the origin (Boussinesq's problem). (C) 2009 Elsevier Ltd. All rights reserved.

【 授权许可】

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